Download Copyright © by Holt, Rinehart and Winston

Name _______________________________________ Date __________________ Class __________________
Reteach
Proving Lines Parallel
If two coplanar lines are cut by a transversal
so that a pair of corresponding angles are
congruent, then the two lines are parallel.
Converse of the Corresponding
Angles Postulate
You can use the Converse of the
Corresponding Angles Postulate
to show that two lines are parallel.
Given:
1
3
1
3
1
q || r
Given: m 2
3 are corresponding angles.
Converse of the Corresponding Angles Postulate
3x°, m 4
(x
50)°, x
m 2
3(25)°
m 4
(25
m 2
m 4
Transitive Property of Equality
4
Definition of congruent angles
2
75°
25
50)°
Substitute 25 for x.
75°
q || r
Substitute 25 for x.
Converse of the Corresponding Angles Postulate
For Exercises 1 and 2, use the Converse of the Corresponding Angles
Postulate and the given information to show that c || d.
1. Given:
2
2. Given: m 1
4
2x°, m 3
(3x
31)°, x
31
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Name _______________________________________ Date __________________ Class __________________
Reteach
Proving Lines Parallel continued
You can also prove that two lines are parallel by using the converse of any of
the other theorems that you learned in Lesson 3-2.
Theorem
Hypothesis
Converse of the Alternate
Interior Angles Theorem
Conclusion
a || b
2
3
Converse of the Alternate
Exterior Angles Theorem
f || g
1
4
Converse of the Same-Side
Interior Angles Theorem
s || t
m 1
m 2
180°
For Exercises 3–5, use the theorems and the given information to
show that j || k.
3. Given:
4
5
4. Given: m 3
12x°, m 5
5. Given: m 2
8x°, m 7
18x°, x
(7x
6
9)°, x
9
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Name _______________________________________ Date __________________ Class __________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry